Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22548738 | C2 | semidirect |
| 2. #30632238 | C2 | semidirect |
| 3. C4×#16860811 | C2 | semidirect |
| 4. #30631911 | C2 | semidirect |
| 5. #30631905 | C2 | semidirect |
| 6. #30631889 | C2 | semidirect |
| 7. #30631887 | C2 | semidirect |
| 8. #30631883 | C2 | semidirect |
| 9. C4⋊C8×D251 | C2 | semidirect |
| 10. #30631682 | C2 | semidirect |
| 11. #462×C251 | C2 | semidirect |
| 47. #16860811 | D4 | semidirect |
| 137. C4×C251 | #135 | semidirect |
| 150. C251 | #3035 | semidirect |
| 157. #462 | D251 | semidirect |
| 292. C4 | #22548738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548738 | 2 |
| #30632238 | 2 |
| C4×#16860811 | 2 |
| #30631911 | 2 |
| #30631905 | 2 |
| #30631889 | 2 |
| #30631887 | 2 |
| #30631883 | 2 |
| C4⋊C8×D251 | 2 |
| #30631682 | 2 |
| #462×C251 | 2 |
| #3035 | 251 |